# Fungrim entry: 325a0e

$\,{}_0{\textbf F}_1\!\left(a, z\right) = {\left(-z\right)}^{\left( 1 - a \right) / 2} J_{a - 1}\!\left(2 \sqrt{-z}\right)$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0$
TeX:
\,{}_0{\textbf F}_1\!\left(a, z\right) = {\left(-z\right)}^{\left( 1 - a \right) / 2} J_{a - 1}\!\left(2 \sqrt{-z}\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
Definitions:
Fungrim symbol Notation Short description
Hypergeometric0F1Regularized$\,{}_0{\textbf F}_1\!\left(a, z\right)$ Regularized confluent hypergeometric limit function
Pow${a}^{b}$ Power
BesselJ$J_{\nu}\!\left(z\right)$ Bessel function of the first kind
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("325a0e"),
Formula(Equal(Hypergeometric0F1Regularized(a, z), Mul(Pow(Neg(z), Div(Sub(1, a), 2)), BesselJ(Sub(a, 1), Mul(2, Sqrt(Neg(z))))))),
Variables(a, z),
Assumptions(And(Element(a, CC), Element(z, CC), NotEqual(z, 0))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC